Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
funk = []
n = int(input())
for i in range(2*int(math.sqrt(n))+1):
    funk.append(i*(i+1)// 2)


i = 1
j = len(funk) - 1

while j >= i:
    if funk[i] + funk[j] > n:
        j -= 1
    elif funk[i] + funk[j] < n:
        i += 1
    else:
        print("YES")
        exit()

print("NO")